Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
$ 0 $ | $=$ | $ x t - 2 x v + y w - y t + y u + 2 y v + z u + 2 z v $ |
| $=$ | $x w + x t - x u - x v - y w + y t + z w - z t + z u + 2 z v$ |
| $=$ | $3 x^{2} + 3 y z + 3 z^{2} - 2 w^{2} + w t - t^{2} - t v + u^{2} + u v + v^{2}$ |
| $=$ | $3 x w - x t + 2 x u + x v - 2 y w - 2 y t - 3 z u$ |
| $=$ | $\cdots$ |
Singular plane model Singular plane model
$ 0 $ | $=$ | $ x^{8} y^{2} - 22 x^{7} y^{3} + 18 x^{7} y z^{2} + 191 x^{6} y^{4} - 249 x^{6} y^{2} z^{2} + \cdots + 1296 y^{2} z^{8} $ |
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Maps to other modular curves
Map
of degree 2 from the canonical model of this modular curve to the canonical model of the modular curve
10.60.3.a.1
:
$\displaystyle X$ |
$=$ |
$\displaystyle -x+3y-z$ |
$\displaystyle Y$ |
$=$ |
$\displaystyle -3x-y+2z$ |
$\displaystyle Z$ |
$=$ |
$\displaystyle -2x+y-2z$ |
Equation of the image curve:
$0$ |
$=$ |
$ 2X^{4}-3X^{3}Y-5X^{2}Y^{2}-4XY^{3}-2Y^{4}+3X^{3}Z-18X^{2}YZ-17XY^{2}Z+4Y^{3}Z-5X^{2}Z^{2}+17XYZ^{2}-6Y^{2}Z^{2}+4XZ^{3}+4YZ^{3}-2Z^{4} $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
60.120.7.a.1
:
$\displaystyle X$ |
$=$ |
$\displaystyle x$ |
$\displaystyle Y$ |
$=$ |
$\displaystyle z$ |
$\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{3}w$ |
Equation of the image curve:
$0$ |
$=$ |
$ X^{8}Y^{2}-22X^{7}Y^{3}+18X^{7}YZ^{2}+191X^{6}Y^{4}-249X^{6}Y^{2}Z^{2}+36X^{6}Z^{4}-816X^{5}Y^{5}+1182X^{5}Y^{3}Z^{2}-612X^{5}YZ^{4}+1719X^{4}Y^{6}-2160X^{4}Y^{4}Z^{2}+2844X^{4}Y^{2}Z^{4}-432X^{4}Z^{6}-1478X^{3}Y^{7}+720X^{3}Y^{5}Z^{2}-1476X^{3}Y^{3}Z^{4}+3456X^{3}YZ^{6}+109X^{2}Y^{8}+2253X^{2}Y^{6}Z^{2}-4572X^{2}Y^{4}Z^{4}-1728X^{2}Y^{2}Z^{6}+1296X^{2}Z^{8}+276XY^{9}-1536XY^{7}Z^{2}+3024XY^{5}Z^{4}+864XY^{3}Z^{6}-2592XYZ^{8}+36Y^{10}-420Y^{8}Z^{2}+1332Y^{6}Z^{4}-2160Y^{4}Z^{6}+1296Y^{2}Z^{8} $ |
This modular curve minimally covers the modular curves listed below.
This modular curve is minimally covered by the modular curves in the database listed below.